Question: The sum of two numbers is $94$, and their difference is $50$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 94}$ ${x-y = 50}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 144 $ $ x = \dfrac{144}{2} $ ${x = 72}$ Now that you know ${x = 72}$ , plug it back into $ {x+y = 94}$ to find $y$ ${(72)}{ + y = 94}$ ${y = 22}$ You can also plug ${x = 72}$ into $ {x-y = 50}$ and get the same answer for $y$ ${(72)}{ - y = 50}$ ${y = 22}$ Therefore, the larger number is $72$, and the smaller number is $22$.